Solution
= Solution
For $T(\rho)=\sum_kp_kU_k\rho U_k^\dagger$,
$$
C_T=\sum_kp_k
(U_k\otimes I)|\phi\rangle\langle\phi|
(U_k^\dagger\otimes I).
$$
Each $(U_k\otimes I)|\phi\rangle$ is a <maximally entangled state>, so the <Choi matrix> is a convex combination of maximally entangled pure states.